Version 2 March 22, 2015 281.273 Assignment 2 Line Coding Lab By: Year 2: Hamilton Milligan ID: 86009447
281.273 Assignment 2 Line Coding Lab 1 OBJECTIVE The Objective of this lab / assignment 2 is to investigate and gain a better understanding of line coding schemes, produce appropriate digital signal waveforms and observe their spectra through the use of MATLAB. 2 SETUP Create a data sequence 1. MATLAB: 2. Num_bits=5 3. data=randint(1,num_bits) 1 UNIPOLAR NRZ SCHEME START UP 1. Map data to voltage levels 1,0,+1 Unipolar_NRZ=data 2. Use script digiwave to plot digiwave(unipolar_nrz,1) 3. Title Plot title('unipolar NZR') 4. To save time, reuse code and ensure we have the same random data to compare later on. The follow script was created: MATLAB code Initialiser Script Results from above Start Up (before initaliser script) 281.273 Assignment 2 Line Coding Lab 1
2.1 UNIPOLAR NRZ Setup data sequence 10 bits and generate Unipolar NZR waveform. The following script was created and run after the initialiser script (see above) 2 POLAR SCHEMES: NRZ L AND NRZ I Generate the polar NRZ L and NRZ I waveforms and compare with unipolar NRZ 2.2 NRZ L POLAR SCHEME 281.273 Assignment 2 Line Coding Lab 2
2.3 NRZ I POLAR SCHEME 2.4 COMPARE NZR L AND NZR I WITH UNIPLOAR Comparision: NRZ L looks like the inverse of Unipolar, but twice the height. NRZ I is harder to understand. 281.273 Assignment 2 Line Coding Lab 3
3 POLAR SCHEME: RZ 3.1 GENERATE A POLAR RZ WAVEFORM AND Polar RZ waveform is represented by two different levels with each level lasting half of the bit duration. 0=> 1 then 0, 1 => +1 then 0 3.2 COMPARE RZ WITH NRZ, NRZ L AND NRZ I Although the markers may seem confusing they do help. I find Polar RZ easier to interpret than NRZ I 281.273 Assignment 2 Line Coding Lab 4
4 POLAR BIPHASE 4.1 MANCHESTER POLAR BIPHASE In Manchester: Each data bit is represented by two different levels with each level lasting half of the bit duration: 0=>+1 then 1 1 => 1 then +1 As a reminder the data used throughout this document (unless stated otherwise) is data = 0 1 1 0 1 0 0 1 1 1 MATLAB code MANCHESTER POLAR BIPHASE Results from data = 0 1 1 0 1 0 0 1 1 1 Comments / Observations: The encoding I have been instructed to do does NOT include a start of ½ cycle of 0 Appears to be Manchester as per IEE 802.3 standards. 4.2 DIFFERENTIAL MANCHESTER POLAR BIPHASE In Differential Manchester: Each data bit is represented by two different levels with each level lasting half of the bit duration: 0=> Invert previous level then previous level 1 => previous level, then inversion of previous level 281.273 Assignment 2 Line Coding Lab 5
MATLAB code: Differential Manchester Polar Biphase Results from data = 0 1 1 0 1 0 0 1 1 1 5 BIPOLAR SCHEMES: AMI AND PSEUDOTERNARY 5.1 AMI BIPOLAR 0=>0, 1=> +1 if previous 1 value is 1, otherwise 1 MATLAB code: Bipolar AMI Results from data = 0 1 1 0 1 0 0 1 1 1 NOTE: Following the rule provided, the first 1 value is 1 as it is "otherwise". If there are long runs of 1's there may be syncing problems. 281.273 Assignment 2 Line Coding Lab 6
5.2 PSEUDOTERNARY 1=>0, 0=> +1 if previous 0 value is 1, otherwise 1 MATLAB code: PSEUDOTERNARY Results from data = 0 1 1 0 1 0 0 1 1 1 NOTE: Very similar to AMI. Major change is that 0 takes on what 1 does in AMI and 1 takes on the role of 0 in AMI. For Pseudoternary if there are long runs of 1's there may be syncing problems. 5.3 TASK 5 1 Find suitable length of the data sequence that we can give meaningful spectrum plot. 2 Write M file that generates a random data sequence of the desired length, 3 performs mapping of various line coding schemes, and plots the spectra of generated digital signals. 4 Compare the spectrum plots with those discussed in the lecture notes. 5.3.1 Find Suitable Length of the data sequence Sampling needs to be at least twice the frequency (Nyquist Criteria).,, 2, is max frequency and is sampling rate. PSD metrics are Power and Frequency. digipsd has set at 2 and sampling. T is basically the length of the data sequence. In the lecture notes there seemed to be no information on best data sequence length. pwelsh in MATLAB does not appear to have the ideal sample size based on excep to say it is an integer multiple of T. So Assuming MATLAB is generating radomly, a population of 120 randomly generated 1 and zeros would produce a sampling rate of 2 Hz and a total number of samples of 120*2 = 240 samples. This should be ample and ensure that the welsh PSD shows a good representation of the actual signal Trying different options, I quite liked 120 for the data sequence. 90 and 60 also worked well. under 50 seemed to become more variable with a wider standard deviation. When sampling the general rule is that the size should be 30 or over. 5.3.2 Write M file see M File in zip file. It is called Lab2Task5.m. to change log y or not, comment out appropriate line in this file within the function digipsdc 281.273 Assignment 2 Line Coding Lab 7
5.3.3 Perform Various mapping of schemes and plot and compare See Lab2Task5.m file. Following is the comparison for the plots with data sequence length of 90. All have the same data. NRZ I is not visible as compared to others as the PSD quickly tends to zero as it has two values, 1 or 1 and the long term average of random generated numbers tends to 0. When changing to log for the y axis, we get the following: 281.273 Assignment 2 Line Coding Lab 8
5.3.4 Compare spectrum with lecture notes Please, I attended all lectures and wrote notes on slides presented. I was not able to compare my results to those in the lecture notes for PSD. As there were no graphs to compare in the notes. The graphs are as I expect on a longer average. Following are all the notes from the lectures concerning sampling and PSD. 281.273 Assignment 2 Line Coding Lab 9
6 SUMMARY Attached files with this document in a zip are: Lab2Task1to4.m Lab2Task5.m. To run with log in y axis, go to function digipsdc and follow comments. Overall a good assignment to action. Step 5 was the most difficult especially with interpretation, as there was nothing in our lectures or notes about this. I suspect my sample size could be reduced form 90 to around 50 to still get a reasonably good plot from random numbers, however I decided to keep with 90 as increasing sample size was with very little expense of computing power and speed. This lab overall to a lot of time to perform and write up. Examples and code provided did help. However showing comparisons in MATLAB did take quite a bit of time to write up. 281.273 Assignment 2 Line Coding Lab 10